LMFDB - Embedded newform 1950.2.y.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.b.199.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.96410 + 1.13397i) q^{17} -1.00000 q^{18} +(1.09808 + 0.633975i) q^{19} -0.732051i q^{21} +(4.09808 + 2.36603i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(0.366025 + 0.633975i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.23205 + 9.06218i) q^{37} -1.26795i q^{38} +(-0.866025 + 3.50000i) q^{39} +(9.86603 - 5.69615i) q^{41} +(-0.633975 + 0.366025i) q^{42} +(6.63397 + 3.83013i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} +8.19615 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-1.00000 - 3.46410i) q^{52} +0.464102i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.366025 - 0.633975i) q^{56} +1.26795 q^{57} +(1.23205 - 2.13397i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(-4.73205 + 2.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(-1.96410 + 1.13397i) q^{68} +(3.09808 - 5.36603i) q^{69} +(-1.09808 - 0.633975i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.73205 q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410i q^{77} +(3.46410 - 1.00000i) q^{78} +9.46410 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.86603 - 5.69615i) q^{82} -10.1962 q^{83} +(0.633975 + 0.366025i) q^{84} -7.66025i q^{86} +(2.13397 + 1.23205i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615i q^{92} +(-2.73205 - 4.73205i) q^{93} +(-4.09808 - 7.09808i) q^{94} +1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33}+ \cdots + 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^11 - 10 * q^13 + 4 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 6 * q^22 + 18 * q^23 + 14 * q^26 - 2 * q^28 - 2 * q^29 - 2 * q^32 - 6 * q^33 + 2 * q^36 + 14 * q^37 + 36 * q^41 - 6 * q^42 + 30 * q^43 - 18 * q^46 + 12 * q^47 + 6 * q^49 + 16 * q^51 - 4 * q^52 - 2 * q^56 + 12 * q^57 - 2 * q^58 + 8 * q^61 - 12 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 6 * q^68 + 2 * q^69 + 6 * q^71 + 2 * q^72 - 32 * q^73 + 14 * q^74 + 6 * q^76 + 24 * q^79 - 2 * q^81 - 36 * q^82 - 20 * q^83 + 6 * q^84 + 12 * q^87 - 6 * q^88 + 12 * q^89 - 4 * q^91 - 4 * q^93 - 6 * q^94 + 12 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	−0.788526	−	0.615002i	$-0.789155\pi$
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	0.926870	+	0.375382i	$0.122489\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.968195	−	0.250196i	$-0.919505\pi$
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.267421	+	0.963580i	$0.586172\pi$
$12$			1.00000i			0.288675i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−0.732051			−0.195649
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.96410	+	1.13397i	0.476365	+	0.275029i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	1.96410	+	1.13397i	0.476365	+	0.275029i	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000			−0.235702
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$		0			0
$21$		−	0.732051i		−	0.159747i
$22$	4.09808	+	2.36603i	0.873713	+	0.504438i
$23$	5.36603	−	3.09808i	1.11889	−	0.645994i	0.177775	−	0.984071i	$-0.443110\pi$
$23$	5.36603	−	3.09808i	1.11889	−	0.645994i	0.941118	+	0.338078i	$0.109777\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$	0.366025	+	0.633975i	0.0691723	+	0.119810i
$29$	1.23205	+	2.13397i	0.228786	+	0.396269i	0.957449	−	0.288604i	$-0.0931910\pi$
$29$	1.23205	+	2.13397i	0.228786	+	0.396269i	−0.728663	+	0.684873i	$0.759858\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.36603	+	4.09808i	−0.411872	+	0.713384i
$34$		−	2.26795i		−	0.388950i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	5.23205	+	9.06218i	0.860144	+	1.48981i	0.871789	+	0.489881i	$0.162960\pi$
$37$	5.23205	+	9.06218i	0.860144	+	1.48981i	−0.0116456	+	0.999932i	$0.503707\pi$
$38$		−	1.26795i		−	0.205689i
$39$	−0.866025	+	3.50000i	−0.138675	+	0.560449i
$40$		0			0
$41$	9.86603	−	5.69615i	1.54081	−	0.889590i	0.542027	−	0.840361i	$-0.317657\pi$
$41$	9.86603	−	5.69615i	1.54081	−	0.889590i	0.998788	−	0.0492283i	$-0.0156762\pi$
$42$	−0.633975	+	0.366025i	−0.0978244	+	0.0564789i
$43$	6.63397	+	3.83013i	1.01167	+	0.584089i	0.911681	−	0.410899i	$-0.134785\pi$
$43$	6.63397	+	3.83013i	1.01167	+	0.584089i	0.0999910	+	0.994988i	$0.468119\pi$
$44$		−	4.73205i		−	0.713384i
$45$		0			0
$46$	−5.36603	−	3.09808i	−0.791177	−	0.456786i
$47$	8.19615			1.19553			0.597766	−	0.801671i	$-0.296055\pi$
$47$	8.19615			1.19553			0.597766	+	0.801671i	$0.296055\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$		0			0
$51$	2.26795			0.317576
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$			0.464102i			0.0637493i	0.999492	+	0.0318746i	$0.0101477\pi$
$53$			0.464102i			0.0637493i	−0.999492	+	0.0318746i	$0.989852\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	0.366025	−	0.633975i	0.0489122	−	0.0847184i
$57$	1.26795			0.167944
$58$	1.23205	−	2.13397i	0.161776	−	0.280205i
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.0241347	−	0.999709i	$-0.507683\pi$
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.877841	+	0.478953i	$0.841016\pi$
$60$		0			0
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	−0.901770	−	0.432215i	$-0.857732\pi$
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	0.825195	+	0.564848i	$0.191065\pi$
$62$	−4.73205	+	2.73205i	−0.600971	+	0.346971i
$63$	−0.366025	−	0.633975i	−0.0461149	−	0.0798733i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	5.56218	+	9.63397i	0.679528	+	1.17698i	0.975123	+	0.221664i	$0.0711488\pi$
$67$	5.56218	+	9.63397i	0.679528	+	1.17698i	−0.295595	+	0.955313i	$0.595518\pi$
$68$	−1.96410	+	1.13397i	−0.238182	+	0.137515i
$69$	3.09808	−	5.36603i	0.372965	−	0.645994i
$70$		0			0
$71$	−1.09808	−	0.633975i	−0.130318	−	0.0752389i	0.433424	−	0.901190i	$-0.357305\pi$
$71$	−1.09808	−	0.633975i	−0.130318	−	0.0752389i	−0.563742	+	0.825951i	$0.690639\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−9.73205			−1.13905			−0.569525	−	0.821974i	$-0.692873\pi$
$73$	−9.73205			−1.13905			−0.569525	+	0.821974i	$0.692873\pi$
$74$	5.23205	−	9.06218i	0.608214	−	1.05346i
$75$		0			0
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$			3.46410i			0.394771i
$78$	3.46410	−	1.00000i	0.392232	−	0.113228i
$79$	9.46410			1.06479			0.532397	−	0.846495i	$-0.321291\pi$
$79$	9.46410			1.06479			0.532397	+	0.846495i	$0.321291\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−9.86603	−	5.69615i	−1.08952	−	0.629035i
$83$	−10.1962			−1.11917			−0.559587	−	0.828772i	$-0.689040\pi$
$83$	−10.1962			−1.11917			−0.559587	+	0.828772i	$0.689040\pi$
$84$	0.633975	+	0.366025i	0.0691723	+	0.0399366i
$85$		0			0
$86$		−	7.66025i		−	0.826026i
$87$	2.13397	+	1.23205i	0.228786	+	0.132090i
$88$	−4.09808	+	2.36603i	−0.436856	+	0.252219i
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		0			0
$91$	0.732051	+	2.53590i	0.0767398	+	0.265834i
$92$			6.19615i			0.645994i
$93$	−2.73205	−	4.73205i	−0.283300	−	0.490691i
$94$	−4.09808	−	7.09808i	−0.422684	−	0.732111i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	3.23205	−	5.59808i	0.326486	−	0.565491i
$99$			4.73205i			0.475589i
$100$		0			0
$101$	−5.96410	−	10.3301i	−0.593450	−	1.02789i	−0.993764	−	0.111508i	$-0.964432\pi$
$101$	−5.96410	−	10.3301i	−0.593450	−	1.02789i	0.400313	−	0.916378i	$-0.368901\pi$
$102$	−1.13397	−	1.96410i	−0.112280	−	0.194475i
$103$			18.7321i			1.84572i	0.385131	+	0.922862i	$0.374156\pi$
$103$			18.7321i			1.84572i	−0.385131	+	0.922862i	$0.625844\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	0.401924	−	0.232051i	0.0390383	−	0.0225388i
$107$	0.169873	−	0.0980762i	0.0164222	−	0.00948139i	−0.491766	−	0.870727i	$-0.663649\pi$
$107$	0.169873	−	0.0980762i	0.0164222	−	0.00948139i	0.508189	+	0.861246i	$0.330315\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			5.46410i			0.523366i	0.965154	+	0.261683i	$0.0842775\pi$
$109$			5.46410i			0.523366i	−0.965154	+	0.261683i	$0.915723\pi$
$110$		0			0
$111$	9.06218	+	5.23205i	0.860144	+	0.496604i
$112$	−0.732051			−0.0691723
$113$	16.1603	+	9.33013i	1.52023	+	0.877705i	0.999716	+	0.0238510i	$0.00759271\pi$
$113$	16.1603	+	9.33013i	1.52023	+	0.877705i	0.520513	+	0.853854i	$0.325741\pi$
$114$	−0.633975	−	1.09808i	−0.0593772	−	0.102844i
$115$		0			0
$116$	−2.46410			−0.228786
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$			8.00000i			0.736460i
$119$	1.43782	−	0.830127i	0.131805	−	0.0760976i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$	1.19615			0.108295
$123$	5.69615	−	9.86603i	0.513605	−	0.889590i
$124$	4.73205	+	2.73205i	0.424951	+	0.245345i
$125$		0			0
$126$	−0.366025	+	0.633975i	−0.0326081	+	0.0564789i
$127$	15.4641	−	8.92820i	1.37222	−	0.792250i	0.381010	−	0.924571i	$-0.375576\pi$
$127$	15.4641	−	8.92820i	1.37222	−	0.792250i	0.991207	+	0.132321i	$0.0422429\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	7.66025			0.674448
$130$		0			0
$131$	13.4641			1.17636			0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641			1.17636			0.588182	+	0.808729i	$0.299844\pi$
$132$	−2.36603	−	4.09808i	−0.205936	−	0.356692i
$133$	0.803848	−	0.464102i	0.0697024	−	0.0402427i
$134$	5.56218	−	9.63397i	0.480499	−	0.832249i
$135$		0			0
$136$	1.96410	+	1.13397i	0.168420	+	0.0972375i
$137$	−0.964102	+	1.66987i	−0.0823688	+	0.142667i	−0.904267	−	0.426968i	$-0.859582\pi$
$137$	−0.964102	+	1.66987i	−0.0823688	+	0.142667i	0.821898	+	0.569634i	$0.192915\pi$
$138$	−6.19615			−0.527452
$139$	−4.92820	+	8.53590i	−0.418005	+	0.724005i	−0.995739	−	0.0922197i	$-0.970604\pi$
$139$	−4.92820	+	8.53590i	−0.418005	+	0.724005i	0.577734	+	0.816225i	$0.303937\pi$
$140$		0			0
$141$	7.09808	−	4.09808i	0.597766	−	0.345120i
$142$			1.26795i			0.106404i
$143$	4.09808	−	16.5622i	0.342698	−	1.38500i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	4.86603	+	8.42820i	0.402715	+	0.697523i
$147$	5.59808	+	3.23205i	0.461722	+	0.266575i
$148$	−10.4641			−0.860144
$149$	2.42820	+	1.40192i	0.198926	+	0.114850i	0.596154	−	0.802870i	$-0.296695\pi$
$149$	2.42820	+	1.40192i	0.198926	+	0.114850i	−0.397228	+	0.917720i	$0.630028\pi$
$150$		0			0
$151$		−	3.26795i		−	0.265942i	−0.991120	−	0.132971i	$-0.957548\pi$
$151$		−	3.26795i		−	0.265942i	0.991120	−	0.132971i	$-0.0424517\pi$
$152$	1.09808	+	0.633975i	0.0890657	+	0.0514221i
$153$	1.96410	−	1.13397i	0.158788	−	0.0916764i
$154$	3.00000	−	1.73205i	0.241747	−	0.139573i
$155$		0			0
$156$	−2.59808	−	2.50000i	−0.208013	−	0.200160i
$157$			23.5885i			1.88256i	0.337622	+	0.941282i	$0.390378\pi$
$157$			23.5885i			1.88256i	−0.337622	+	0.941282i	$0.609622\pi$
$158$	−4.73205	−	8.19615i	−0.376462	−	0.652051i
$159$	0.232051	+	0.401924i	0.0184028	+	0.0318746i
$160$		0			0
$161$		−	4.53590i		−	0.357479i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.26795	−	5.66025i	0.255966	−	0.443345i	−0.709192	−	0.705016i	$-0.750940\pi$
$163$	3.26795	−	5.66025i	0.255966	−	0.443345i	0.965157	+	0.261670i	$0.0842733\pi$
$164$			11.3923i			0.889590i
$165$		0			0
$166$	5.09808	+	8.83013i	0.395687	+	0.685351i
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	0.812788	−	0.582559i	$-0.197949\pi$
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	−0.910905	+	0.412616i	$0.864615\pi$
$168$		−	0.732051i		−	0.0564789i
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	1.09808	−	0.633975i	0.0839720	−	0.0484812i
$172$	−6.63397	+	3.83013i	−0.505836	+	0.292044i
$173$	−14.1962	−	8.19615i	−1.07931	−	0.623142i	−0.148602	−	0.988897i	$-0.547477\pi$
$173$	−14.1962	−	8.19615i	−1.07931	−	0.623142i	−0.930711	+	0.365755i	$0.880811\pi$
$174$		−	2.46410i		−	0.186803i
$175$		0			0
$176$	4.09808	+	2.36603i	0.308904	+	0.178346i
$177$	−8.00000			−0.601317
$178$	2.19615	+	1.26795i	0.164609	+	0.0950368i
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	−0.902573	−	0.430538i	$-0.858324\pi$
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	0.0784298	−	0.996920i	$-0.475009\pi$
$180$		0			0
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$	1.83013	−	1.90192i	0.135658	−	0.140980i
$183$			1.19615i			0.0884221i
$184$	5.36603	−	3.09808i	0.395589	−	0.228393i
$185$		0			0
$186$	−2.73205	+	4.73205i	−0.200324	+	0.346971i
$187$	−10.7321			−0.784805
$188$	−4.09808	+	7.09808i	−0.298883	+	0.517680i
$189$	−0.633975	−	0.366025i	−0.0461149	−	0.0266244i
$190$		0			0
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	−0.963706	−	0.266966i	$-0.913979\pi$
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	0.713052	+	0.701111i	$0.247312\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	4.13397	+	7.16025i	0.297570	+	0.515406i	0.975579	−	0.219647i	$-0.0704905\pi$
$193$	4.13397	+	7.16025i	0.297570	+	0.515406i	−0.678009	+	0.735053i	$0.737157\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	0.635326	−	0.772244i	$-0.280866\pi$
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	−0.986446	+	0.164086i	$0.947532\pi$
$198$	4.09808	−	2.36603i	0.291238	−	0.168146i
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	−0.790706	−	0.612196i	$-0.790286\pi$
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	0.925530	+	0.378674i	$0.123620\pi$
$200$		0			0
$201$	9.63397	+	5.56218i	0.679528	+	0.392326i
$202$	−5.96410	+	10.3301i	−0.419633	+	0.726825i
$203$	1.80385			0.126605
$204$	−1.13397	+	1.96410i	−0.0793941	+	0.137515i
$205$		0			0
$206$	16.2224	−	9.36603i	1.13027	−	0.652562i
$207$		−	6.19615i		−	0.430662i
$208$	3.50000	+	0.866025i	0.242681	+	0.0600481i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	0.931665	−	0.363319i	$-0.118356\pi$
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	−0.780476	+	0.625186i	$0.785023\pi$
$212$	−0.401924	−	0.232051i	−0.0276042	−	0.0159373i
$213$	−1.26795			−0.0868784
$214$	−0.169873	−	0.0980762i	−0.0116123	−	0.00670435i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−3.46410	−	2.00000i	−0.235159	−	0.135769i
$218$	4.73205	−	2.73205i	0.320495	−	0.185038i
$219$	−8.42820	+	4.86603i	−0.569525	+	0.328816i
$220$		0			0
$221$	−7.85641	+	2.26795i	−0.528479	+	0.152559i
$222$		−	10.4641i		−	0.702305i
$223$	−6.53590	−	11.3205i	−0.437676	−	0.758077i	0.559834	−	0.828605i	$-0.310865\pi$
$223$	−6.53590	−	11.3205i	−0.437676	−	0.758077i	−0.997510	+	0.0705277i	$0.977532\pi$
$224$	0.366025	+	0.633975i	0.0244561	+	0.0423592i
$225$		0			0
$226$		−	18.6603i		−	1.24126i
$227$	0.901924	−	1.56218i	0.0598628	−	0.103685i	−0.834541	−	0.550946i	$-0.814267\pi$
$227$	0.901924	−	1.56218i	0.0598628	−	0.103685i	0.894404	+	0.447261i	$0.147600\pi$
$228$	−0.633975	+	1.09808i	−0.0419860	+	0.0727219i
$229$			15.8564i			1.04782i	0.851773	+	0.523910i	$0.175527\pi$
$229$			15.8564i			1.04782i	−0.851773	+	0.523910i	$0.824473\pi$
$230$		0			0
$231$	1.73205	+	3.00000i	0.113961	+	0.197386i
$232$	1.23205	+	2.13397i	0.0808881	+	0.140102i
$233$		−	19.8564i		−	1.30084i	−0.759576	−	0.650418i	$-0.774594\pi$
$233$		−	19.8564i		−	1.30084i	0.759576	−	0.650418i	$-0.225406\pi$
$234$	2.50000	−	2.59808i	0.163430	−	0.169842i
$235$		0			0
$236$	6.92820	−	4.00000i	0.450988	−	0.260378i
$237$	8.19615	−	4.73205i	0.532397	−	0.307380i
$238$	−1.43782	−	0.830127i	−0.0932002	−	0.0538091i
$239$			9.66025i			0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$			9.66025i			0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$		0			0
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.0785557	−	0.996910i	$-0.525031\pi$
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.902627	+	0.430424i	$0.858364\pi$
$242$	−11.3923			−0.732325
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.598076	−	1.03590i	−0.0382879	−	0.0663166i
$245$		0			0
$246$	−11.3923			−0.726347
$247$	−4.39230	+	1.26795i	−0.279476	+	0.0806777i
$248$		−	5.46410i		−	0.346971i
$249$	−8.83013	+	5.09808i	−0.559587	+	0.323077i
$250$		0			0
$251$	3.26795	−	5.66025i	0.206271	−	0.357272i	−0.744266	−	0.667883i	$-0.767200\pi$
$251$	3.26795	−	5.66025i	0.206271	−	0.357272i	0.950537	+	0.310611i	$0.100534\pi$
$252$	0.732051			0.0461149
$253$	−14.6603	+	25.3923i	−0.921682	+	1.59640i
$254$	−15.4641	−	8.92820i	−0.970304	−	0.560205i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.0885	−	13.3301i	1.44022	−	0.831510i	0.442355	−	0.896840i	$-0.354143\pi$
$257$	23.0885	−	13.3301i	1.44022	−	0.831510i	0.997864	+	0.0653297i	$0.0208099\pi$
$258$	−3.83013	−	6.63397i	−0.238453	−	0.413013i
$259$	7.66025			0.475985
$260$		0			0
$261$	2.46410			0.152524
$262$	−6.73205	−	11.6603i	−0.415907	−	0.720373i
$263$	24.2942	−	14.0263i	1.49805	−	0.864897i	0.498049	−	0.867149i	$-0.334050\pi$
$263$	24.2942	−	14.0263i	1.49805	−	0.864897i	0.999997	+	0.00225153i	$0.000716686\pi$
$264$	−2.36603	+	4.09808i	−0.145619	+	0.252219i
$265$		0			0
$266$	−0.803848	−	0.464102i	−0.0492871	−	0.0284559i
$267$	−1.26795	+	2.19615i	−0.0775972	+	0.134402i
$268$	−11.1244			−0.679528
$269$	−0.732051	+	1.26795i	−0.0446339	+	0.0773082i	−0.887479	−	0.460848i	$-0.847545\pi$
$269$	−0.732051	+	1.26795i	−0.0446339	+	0.0773082i	0.842845	+	0.538156i	$0.180879\pi$
$270$		0			0
$271$	−5.07180	+	2.92820i	−0.308090	+	0.177876i	−0.646071	−	0.763277i	$-0.723589\pi$
$271$	−5.07180	+	2.92820i	−0.308090	+	0.177876i	0.337982	+	0.941153i	$0.390256\pi$
$272$		−	2.26795i		−	0.137515i
$273$	1.90192	+	1.83013i	0.115110	+	0.110764i
$274$	1.92820			0.116487
$275$		0			0
$276$	3.09808	+	5.36603i	0.186482	+	0.322997i
$277$	1.96410	+	1.13397i	0.118011	+	0.0681339i	0.557844	−	0.829946i	$-0.311629\pi$
$277$	1.96410	+	1.13397i	0.118011	+	0.0681339i	−0.439832	+	0.898080i	$0.644962\pi$
$278$	9.85641			0.591148
$279$	−4.73205	−	2.73205i	−0.283300	−	0.163564i
$280$		0			0
$281$			22.3205i			1.33153i	0.746162	+	0.665765i	$0.231895\pi$
$281$			22.3205i			1.33153i	−0.746162	+	0.665765i	$0.768105\pi$
$282$	−7.09808	−	4.09808i	−0.422684	−	0.244037i
$283$	−7.22243	+	4.16987i	−0.429329	+	0.247873i	−0.699061	−	0.715062i	$-0.746398\pi$
$283$	−7.22243	+	4.16987i	−0.429329	+	0.247873i	0.269732	+	0.962936i	$0.413065\pi$
$284$	1.09808	−	0.633975i	0.0651588	−	0.0376195i
$285$		0			0
$286$	−16.3923	+	4.73205i	−0.969297	+	0.279812i
$287$		−	8.33975i		−	0.492280i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−5.92820	−	10.2679i	−0.348718	−	0.603997i
$290$		0			0
$291$		−	6.00000i		−	0.351726i
$292$	4.86603	−	8.42820i	0.284763	−	0.493223i
$293$	7.25833	−	12.5718i	0.424036	−	0.734452i	−0.572294	−	0.820049i	$-0.693946\pi$
$293$	7.25833	−	12.5718i	0.424036	−	0.734452i	0.996330	+	0.0855965i	$0.0272796\pi$
$294$		−	6.46410i		−	0.376994i
$295$		0			0
$296$	5.23205	+	9.06218i	0.304107	+	0.526728i
$297$	2.36603	+	4.09808i	0.137291	+	0.237795i
$298$		−	2.80385i		−	0.162423i
$299$	−5.36603	+	21.6865i	−0.310325	+	1.25416i
$300$		0			0
$301$	4.85641	−	2.80385i	0.279919	−	0.161611i
$302$	−2.83013	+	1.63397i	−0.162856	+	0.0940247i
$303$	−10.3301	−	5.96410i	−0.593450	−	0.342629i
$304$		−	1.26795i		−	0.0727219i
$305$		0			0
$306$	−1.96410	−	1.13397i	−0.112280	−	0.0648250i
$307$	−8.58846			−0.490169			−0.245085	−	0.969502i	$-0.578816\pi$
$307$	−8.58846			−0.490169			−0.245085	+	0.969502i	$0.578816\pi$
$308$	−3.00000	−	1.73205i	−0.170941	−	0.0986928i
$309$	9.36603	+	16.2224i	0.532815	+	0.922862i
$310$		0			0
$311$	−15.6603			−0.888012			−0.444006	−	0.896024i	$-0.646443\pi$
$311$	−15.6603			−0.888012			−0.444006	+	0.896024i	$0.646443\pi$
$312$	−0.866025	+	3.50000i	−0.0490290	+	0.198148i
$313$			13.4641i			0.761036i	0.924774	+	0.380518i	$0.124254\pi$
$313$			13.4641i			0.761036i	−0.924774	+	0.380518i	$0.875746\pi$
$314$	20.4282	−	11.7942i	1.15283	−	0.665587i
$315$		0			0
$316$	−4.73205	+	8.19615i	−0.266199	+	0.461070i
$317$	3.33975			0.187579			0.0937894	−	0.995592i	$-0.470102\pi$
$317$	3.33975			0.187579			0.0937894	+	0.995592i	$0.470102\pi$
$318$	0.232051	−	0.401924i	0.0130128	−	0.0225388i
$319$	−10.0981	−	5.83013i	−0.565384	−	0.326424i
$320$		0			0
$321$	0.0980762	−	0.169873i	0.00547408	−	0.00948139i
$322$	−3.92820	+	2.26795i	−0.218910	+	0.126388i
$323$	1.43782	+	2.49038i	0.0800026	+	0.138569i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.53590			−0.361990
$327$	2.73205	+	4.73205i	0.151083	+	0.261683i
$328$	9.86603	−	5.69615i	0.544760	−	0.314517i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.0583130	−	0.998298i	$-0.518572\pi$
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.893708	+	0.448649i	$0.851905\pi$
$332$	5.09808	−	8.83013i	0.279793	−	0.484616i
$333$	10.4641			0.573429
$334$	−1.26795	+	2.19615i	−0.0693791	+	0.120168i
$335$		0			0
$336$	−0.633975	+	0.366025i	−0.0345861	+	0.0199683i
$337$			6.85641i			0.373492i	0.982408	+	0.186746i	$0.0597942\pi$
$337$			6.85641i			0.373492i	−0.982408	+	0.186746i	$0.940206\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	18.6603			1.01349
$340$		0			0
$341$	12.9282	+	22.3923i	0.700101	+	1.21261i
$342$	−1.09808	−	0.633975i	−0.0593772	−	0.0342814i
$343$	9.85641			0.532196
$344$	6.63397	+	3.83013i	0.357680	+	0.206507i
$345$		0			0
$346$			16.3923i			0.881256i
$347$	7.68653	+	4.43782i	0.412635	+	0.238235i	0.691921	−	0.721973i	$-0.256765\pi$
$347$	7.68653	+	4.43782i	0.412635	+	0.238235i	−0.279286	+	0.960208i	$0.590098\pi$
$348$	−2.13397	+	1.23205i	−0.114393	+	0.0660449i
$349$	−16.7321	+	9.66025i	−0.895646	+	0.517102i	−0.875785	−	0.482701i	$-0.839656\pi$
$349$	−16.7321	+	9.66025i	−0.895646	+	0.517102i	−0.0198610	+	0.999803i	$0.506322\pi$
$350$		0			0
$351$	2.59808	+	2.50000i	0.138675	+	0.133440i
$352$		−	4.73205i		−	0.252219i
$353$	9.89230	+	17.1340i	0.526514	+	0.911949i	0.999523	+	0.0308916i	$0.00983466\pi$
$353$	9.89230	+	17.1340i	0.526514	+	0.911949i	−0.473008	+	0.881058i	$0.656832\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$		0			0
$356$		−	2.53590i		−	0.134402i
$357$	0.830127	−	1.43782i	0.0439350	−	0.0760976i
$358$	−11.0263	+	19.0981i	−0.582757	+	1.00936i
$359$			23.1244i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$			23.1244i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	4.40192	+	7.62436i	0.231360	+	0.400727i
$363$		−	11.3923i		−	0.597941i
$364$	−2.56218	−	0.633975i	−0.134295	−	0.0332293i
$365$		0			0
$366$	1.03590	−	0.598076i	0.0541473	−	0.0312619i
$367$	12.7583	−	7.36603i	0.665979	−	0.384503i	−0.128572	−	0.991700i	$-0.541039\pi$
$367$	12.7583	−	7.36603i	0.665979	−	0.384503i	0.794551	+	0.607197i	$0.207706\pi$
$368$	−5.36603	−	3.09808i	−0.279723	−	0.161498i
$369$		−	11.3923i		−	0.593060i
$370$		0			0
$371$	0.294229	+	0.169873i	0.0152756	+	0.00881937i
$372$	5.46410			0.283300
$373$	8.89230	+	5.13397i	0.460426	+	0.265827i	0.712223	−	0.701953i	$-0.247688\pi$
$373$	8.89230	+	5.13397i	0.460426	+	0.265827i	−0.251797	+	0.967780i	$0.581022\pi$
$374$	5.36603	+	9.29423i	0.277471	+	0.480593i
$375$		0			0
$376$	8.19615			0.422684
$377$	−8.62436	−	2.13397i	−0.444177	−	0.109905i
$378$			0.732051i			0.0376526i
$379$	−1.26795	+	0.732051i	−0.0651302	+	0.0376029i	−0.532211	−	0.846611i	$-0.678639\pi$
$379$	−1.26795	+	0.732051i	−0.0651302	+	0.0376029i	0.467081	+	0.884214i	$0.345306\pi$
$380$		0			0
$381$	8.92820	−	15.4641i	0.457406	−	0.792250i
$382$	6.92820			0.354478
$383$	2.73205	−	4.73205i	0.139601	−	0.241797i	−0.787744	−	0.616002i	$-0.788751\pi$
$383$	2.73205	−	4.73205i	0.139601	−	0.241797i	0.927346	+	0.374206i	$0.122085\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	4.13397	−	7.16025i	0.210414	−	0.364447i
$387$	6.63397	−	3.83013i	0.337224	−	0.194696i
$388$	3.00000	+	5.19615i	0.152302	+	0.263795i
$389$	−29.7846			−1.51014			−0.755070	−	0.655644i	$-0.772397\pi$
$389$	−29.7846			−1.51014			−0.755070	+	0.655644i	$0.772397\pi$
$390$		0			0
$391$	14.0526			0.710668
$392$	3.23205	+	5.59808i	0.163243	+	0.282746i
$393$	11.6603	−	6.73205i	0.588182	−	0.339587i
$394$	−4.92820	+	8.53590i	−0.248279	+	0.430032i
$395$		0			0
$396$	−4.09808	−	2.36603i	−0.205936	−	0.118897i
$397$	−0.196152	+	0.339746i	−0.00984461	+	0.0170514i	−0.870906	−	0.491450i	$-0.836467\pi$
$397$	−0.196152	+	0.339746i	−0.00984461	+	0.0170514i	0.861061	+	0.508501i	$0.169800\pi$
$398$	−3.80385			−0.190670
$399$	0.464102	−	0.803848i	0.0232341	−	0.0402427i
$400$		0			0
$401$	−18.9904	+	10.9641i	−0.948334	+	0.547521i	−0.892563	−	0.450922i	$-0.851095\pi$
$401$	−18.9904	+	10.9641i	−0.948334	+	0.547521i	−0.0557713	+	0.998444i	$0.517762\pi$
$402$		−	11.1244i		−	0.554832i
$403$	14.1962	+	13.6603i	0.707161	+	0.680466i
$404$	11.9282			0.593450
$405$		0			0
$406$	−0.901924	−	1.56218i	−0.0447617	−	0.0775296i
$407$	−42.8827	−	24.7583i	−2.12562	−	1.22722i
$408$	2.26795			0.112280
$409$	12.3564	+	7.13397i	0.610985	+	0.352752i	0.773351	−	0.633978i	$-0.218579\pi$
$409$	12.3564	+	7.13397i	0.610985	+	0.352752i	−0.162366	+	0.986731i	$0.551912\pi$
$410$		0			0
$411$			1.92820i			0.0951113i
$412$	−16.2224	−	9.36603i	−0.799222	−	0.461431i
$413$	−5.07180	+	2.92820i	−0.249567	+	0.144087i
$414$	−5.36603	+	3.09808i	−0.263726	+	0.152262i
$415$		0			0
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$			9.85641i			0.482670i
$418$	3.00000	+	5.19615i	0.146735	+	0.254152i
$419$	−5.26795	−	9.12436i	−0.257356	−	0.445754i	0.708177	−	0.706035i	$-0.249518\pi$
$419$	−5.26795	−	9.12436i	−0.257356	−	0.445754i	−0.965533	+	0.260281i	$0.916185\pi$
$420$		0			0
$421$			32.7128i			1.59432i	0.603765	+	0.797162i	$0.293667\pi$
$421$			32.7128i			1.59432i	−0.603765	+	0.797162i	$0.706333\pi$
$422$	2.19615	−	3.80385i	0.106907	−	0.185168i
$423$	4.09808	−	7.09808i	0.199255	−	0.345120i
$424$			0.464102i			0.0225388i
$425$		0			0
$426$	0.633975	+	1.09808i	0.0307162	+	0.0532020i
$427$	0.437822	+	0.758330i	0.0211877	+	0.0366982i
$428$			0.196152i			0.00948139i
$429$	−4.73205	−	16.3923i	−0.228466	−	0.791428i
$430$		0			0
$431$	−9.63397	+	5.56218i	−0.464052	+	0.267921i	−0.713747	−	0.700404i	$-0.753003\pi$
$431$	−9.63397	+	5.56218i	−0.464052	+	0.267921i	0.249694	+	0.968325i	$0.419670\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−12.8660	−	7.42820i	−0.618302	−	0.356977i	0.157906	−	0.987454i	$-0.449526\pi$
$433$	−12.8660	−	7.42820i	−0.618302	−	0.356977i	−0.776208	+	0.630478i	$0.782859\pi$
$434$			4.00000i			0.192006i
$435$		0			0
$436$	−4.73205	−	2.73205i	−0.226624	−	0.130842i
$437$	7.85641			0.375823
$438$	8.42820	+	4.86603i	0.402715	+	0.232508i
$439$	8.83013	+	15.2942i	0.421439	+	0.729954i	0.996080	−	0.0884515i	$-0.0281918\pi$
$439$	8.83013	+	15.2942i	0.421439	+	0.729954i	−0.574642	+	0.818405i	$0.694859\pi$
$440$		0			0
$441$	6.46410			0.307814
$442$	5.89230	+	5.66987i	0.280268	+	0.269688i
$443$			36.3923i			1.72905i	0.502589	+	0.864525i	$0.332381\pi$
$443$			36.3923i			1.72905i	−0.502589	+	0.864525i	$0.667619\pi$
$444$	−9.06218	+	5.23205i	−0.430072	+	0.248302i
$445$		0			0
$446$	−6.53590	+	11.3205i	−0.309484	+	0.536042i
$447$	2.80385			0.132617
$448$	0.366025	−	0.633975i	0.0172931	−	0.0299525i
$449$	20.1962	+	11.6603i	0.953115	+	0.550281i	0.894047	−	0.447973i	$-0.147854\pi$
$449$	20.1962	+	11.6603i	0.953115	+	0.550281i	0.0590680	+	0.998254i	$0.481187\pi$
$450$		0			0
$451$	−26.9545	+	46.6865i	−1.26924	+	2.19838i
$452$	−16.1603	+	9.33013i	−0.760114	+	0.438852i
$453$	−1.63397	−	2.83013i	−0.0767708	−	0.132971i
$454$	−1.80385			−0.0846588
$455$		0			0
$456$	1.26795			0.0593772
$457$	−9.33013	−	16.1603i	−0.436445	−	0.755945i	0.560967	−	0.827838i	$-0.310429\pi$
$457$	−9.33013	−	16.1603i	−0.436445	−	0.755945i	−0.997412	+	0.0718931i	$0.977096\pi$
$458$	13.7321	−	7.92820i	0.641657	−	0.370461i
$459$	1.13397	−	1.96410i	0.0529294	−	0.0916764i
$460$		0			0
$461$	−22.2846	−	12.8660i	−1.03790	−	0.599231i	−0.118661	−	0.992935i	$-0.537860\pi$
$461$	−22.2846	−	12.8660i	−1.03790	−	0.599231i	−0.919237	+	0.393704i	$0.871193\pi$
$462$	1.73205	−	3.00000i	0.0805823	−	0.139573i
$463$	−28.0526			−1.30371			−0.651856	−	0.758342i	$-0.726010\pi$
$463$	−28.0526			−1.30371			−0.651856	+	0.758342i	$0.726010\pi$
$464$	1.23205	−	2.13397i	0.0571965	−	0.0990673i
$465$		0			0
$466$	−17.1962	+	9.92820i	−0.796596	+	0.459915i
$467$		−	12.5885i		−	0.582524i	−0.956643	−	0.291262i	$-0.905925\pi$
$467$		−	12.5885i		−	0.582524i	0.956643	−	0.291262i	$-0.0940752\pi$
$468$	−3.50000	−	0.866025i	−0.161788	−	0.0400320i
$469$	8.14359			0.376036
$470$		0			0
$471$	11.7942	+	20.4282i	0.543449	+	0.941282i
$472$	−6.92820	−	4.00000i	−0.318896	−	0.184115i
$473$	−36.2487			−1.66672
$474$	−8.19615	−	4.73205i	−0.376462	−	0.217350i
$475$		0			0
$476$			1.66025i			0.0760976i
$477$	0.401924	+	0.232051i	0.0184028	+	0.0106249i
$478$	8.36603	−	4.83013i	0.382653	−	0.220925i
$479$	22.9808	−	13.2679i	1.05002	−	0.606228i	0.127363	−	0.991856i	$-0.459349\pi$
$479$	22.9808	−	13.2679i	1.05002	−	0.606228i	0.922654	+	0.385628i	$0.126015\pi$
$480$		0			0
$481$	−36.6244	−	9.06218i	−1.66993	−	0.413200i
$482$			17.5885i			0.801132i
$483$	−2.26795	−	3.92820i	−0.103195	−	0.178739i
$484$	5.69615	+	9.86603i	0.258916	+	0.448456i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−10.5622	+	18.2942i	−0.478618	+	0.828991i	−0.999699	−	0.0245163i	$-0.992195\pi$
$487$	−10.5622	+	18.2942i	−0.478618	+	0.828991i	0.521081	+	0.853507i	$0.325529\pi$
$488$	−0.598076	+	1.03590i	−0.0270736	+	0.0468929i
$489$		−	6.53590i		−	0.295564i
$490$		0			0
$491$	2.63397	+	4.56218i	0.118870	+	0.205888i	0.919320	−	0.393511i	$-0.128740\pi$
$491$	2.63397	+	4.56218i	0.118870	+	0.205888i	−0.800450	+	0.599399i	$0.795406\pi$
$492$	5.69615	+	9.86603i	0.256802	+	0.444795i
$493$			5.58846i			0.251691i
$494$	3.29423	+	3.16987i	0.148214	+	0.142619i
$495$		0			0
$496$	−4.73205	+	2.73205i	−0.212475	+	0.122673i
$497$	−0.803848	+	0.464102i	−0.0360575	+	0.0208178i
$498$	8.83013	+	5.09808i	0.395687	+	0.228450i
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$		0			0
$501$	−2.19615	−	1.26795i	−0.0981169	−	0.0566478i
$502$	−6.53590			−0.291711
$503$	9.50962	+	5.49038i	0.424013	+	0.244804i	0.696793	−	0.717272i	$-0.254610\pi$
$503$	9.50962	+	5.49038i	0.424013	+	0.244804i	−0.272780	+	0.962076i	$0.587943\pi$
$504$	−0.366025	−	0.633975i	−0.0163041	−	0.0282395i
$505$		0			0
$506$	29.3205			1.30346
$507$	−6.92820	−	11.0000i	−0.307692	−	0.488527i
$508$			17.8564i			0.792250i
$509$	−8.89230	+	5.13397i	−0.394144	+	0.227559i	−0.683954	−	0.729525i	$-0.739741\pi$
$509$	−8.89230	+	5.13397i	−0.394144	+	0.227559i	0.289810	+	0.957084i	$0.406408\pi$
$510$		0			0
$511$	−3.56218	+	6.16987i	−0.157581	+	0.272939i
$512$	1.00000			0.0441942
$513$	0.633975	−	1.09808i	0.0279907	−	0.0484812i
$514$	−23.0885	−	13.3301i	−1.01839	−	0.587967i
$515$		0			0
$516$	−3.83013	+	6.63397i	−0.168612	+	0.292044i
$517$	−33.5885	+	19.3923i	−1.47722	+	0.852873i
$518$	−3.83013	−	6.63397i	−0.168286	−	0.291480i
$519$	−16.3923			−0.719542
$520$		0			0
$521$	−17.4449			−0.764273			−0.382137	−	0.924106i	$-0.624812\pi$
$521$	−17.4449			−0.764273			−0.382137	+	0.924106i	$0.624812\pi$
$522$	−1.23205	−	2.13397i	−0.0539254	−	0.0934015i
$523$	31.5622	−	18.2224i	1.38012	−	0.796811i	0.387945	−	0.921683i	$-0.373185\pi$
$523$	31.5622	−	18.2224i	1.38012	−	0.796811i	0.992173	+	0.124871i	$0.0398518\pi$
$524$	−6.73205	+	11.6603i	−0.294091	+	0.509381i
$525$		0			0
$526$	−24.2942	−	14.0263i	−1.05928	−	0.611575i
$527$	6.19615	−	10.7321i	0.269909	−	0.467495i
$528$	4.73205			0.205936
$529$	7.69615	−	13.3301i	0.334615	−	0.579571i
$530$		0			0
$531$	−6.92820	+	4.00000i	−0.300658	+	0.173585i
$532$			0.928203i			0.0402427i
$533$	−9.86603	+	39.8731i	−0.427345	+	1.72709i
$534$	2.53590			0.109739
$535$		0			0
$536$	5.56218	+	9.63397i	0.240249	+	0.416124i
$537$	−19.0981	−	11.0263i	−0.824143	−	0.475819i
$538$	1.46410			0.0631219
$539$	−26.4904	−	15.2942i	−1.14102	−	0.658769i
$540$		0			0
$541$		−	40.3205i		−	1.73351i	−0.498731	−	0.866757i	$-0.666200\pi$
$541$		−	40.3205i		−	1.73351i	0.498731	−	0.866757i	$-0.333800\pi$
$542$	5.07180	+	2.92820i	0.217852	+	0.125777i
$543$	−7.62436	+	4.40192i	−0.327192	+	0.188905i
$544$	−1.96410	+	1.13397i	−0.0842102	+	0.0486188i
$545$		0			0
$546$	0.633975	−	2.56218i	0.0271316	−	0.109651i
$547$		−	6.19615i		−	0.264928i	−0.991188	−	0.132464i	$-0.957711\pi$
$547$		−	6.19615i		−	0.264928i	0.991188	−	0.132464i	$-0.0422889\pi$
$548$	−0.964102	−	1.66987i	−0.0411844	−	0.0713334i
$549$	0.598076	+	1.03590i	0.0255253	+	0.0442111i
$550$		0			0
$551$			3.12436i			0.133102i
$552$	3.09808	−	5.36603i	0.131863	−	0.228393i
$553$	3.46410	−	6.00000i	0.147309	−	0.255146i
$554$		−	2.26795i		−	0.0963559i
$555$		0			0
$556$	−4.92820	−	8.53590i	−0.209002	−	0.362003i
$557$	−15.1865	−	26.3038i	−0.643474	−	1.11453i	−0.984652	−	0.174531i	$-0.944159\pi$
$557$	−15.1865	−	26.3038i	−0.643474	−	1.11453i	0.341178	−	0.939999i	$-0.389174\pi$
$558$			5.46410i			0.231314i
$559$	−26.5359	+	7.66025i	−1.12235	+	0.323994i
$560$		0			0
$561$	−9.29423	+	5.36603i	−0.392403	+	0.226554i
$562$	19.3301	−	11.1603i	0.815392	−	0.470767i
$563$	18.2487	+	10.5359i	0.769091	+	0.444035i	0.832550	−	0.553949i	$-0.186880\pi$
$563$	18.2487	+	10.5359i	0.769091	+	0.444035i	−0.0634589	+	0.997984i	$0.520213\pi$
$564$			8.19615i			0.345120i
$565$		0			0
$566$	7.22243	+	4.16987i	0.303581	+	0.175273i
$567$	−0.732051			−0.0307432
$568$	−1.09808	−	0.633975i	−0.0460743	−	0.0266010i
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	0.912893	+	0.408200i	$0.133843\pi$
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	−0.102935	+	0.994688i	$0.532823\pi$
$570$		0			0
$571$	24.0526			1.00657			0.503284	−	0.864121i	$-0.332125\pi$
$571$	24.0526			1.00657			0.503284	+	0.864121i	$0.332125\pi$
$572$	12.2942	+	11.8301i	0.514048	+	0.494642i
$573$			6.92820i			0.289430i
$574$	−7.22243	+	4.16987i	−0.301458	+	0.174047i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	0.267949			0.0111549			0.00557744	−	0.999984i	$-0.498225\pi$
$577$	0.267949			0.0111549			0.00557744	+	0.999984i	$0.498225\pi$
$578$	−5.92820	+	10.2679i	−0.246581	+	0.427090i
$579$	7.16025	+	4.13397i	0.297570	+	0.171802i
$580$		0			0
$581$	−3.73205	+	6.46410i	−0.154832	+	0.268176i
$582$	−5.19615	+	3.00000i	−0.215387	+	0.124354i
$583$	−1.09808	−	1.90192i	−0.0454777	−	0.0787696i
$584$	−9.73205			−0.402715
$585$		0			0
$586$	−14.5167			−0.599678
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	0.652355	−	0.757914i	$-0.273781\pi$
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	−0.982550	+	0.185999i	$0.940448\pi$
$588$	−5.59808	+	3.23205i	−0.230861	+	0.133288i
$589$	3.46410	−	6.00000i	0.142736	−	0.247226i
$590$		0			0
$591$	−8.53590	−	4.92820i	−0.351120	−	0.202719i
$592$	5.23205	−	9.06218i	0.215036	−	0.372453i
$593$	−36.8564			−1.51351			−0.756756	−	0.653698i	$-0.773217\pi$
$593$	−36.8564			−1.51351			−0.756756	+	0.653698i	$0.773217\pi$
$594$	2.36603	−	4.09808i	0.0970792	−	0.168146i
$595$		0			0
$596$	−2.42820	+	1.40192i	−0.0994631	+	0.0574250i
$597$		−	3.80385i		−	0.155681i
$598$	21.4641	−	6.19615i	0.877732	−	0.253380i
$599$	9.46410			0.386693			0.193346	−	0.981131i	$-0.438066\pi$
$599$	9.46410			0.386693			0.193346	+	0.981131i	$0.438066\pi$
$600$		0			0
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	0.920126	−	0.391622i	$-0.128086\pi$
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	−0.799218	+	0.601041i	$0.794753\pi$
$602$	−4.85641	−	2.80385i	−0.197932	−	0.114276i
$603$	11.1244			0.453019
$604$	2.83013	+	1.63397i	0.115156	+	0.0664855i
$605$		0			0
$606$			11.9282i			0.484550i
$607$	0.679492	+	0.392305i	0.0275797	+	0.0159232i	0.513726	−	0.857954i	$-0.328265\pi$
$607$	0.679492	+	0.392305i	0.0275797	+	0.0159232i	−0.486147	+	0.873877i	$0.661598\pi$
$608$	−1.09808	+	0.633975i	−0.0445329	+	0.0257111i
$609$	1.56218	−	0.901924i	0.0633026	−	0.0365478i
$610$		0			0
$611$	−20.4904	+	21.2942i	−0.828952	+	0.861472i
$612$			2.26795i			0.0916764i
$613$	5.69615	+	9.86603i	0.230065	+	0.398485i	0.957827	−	0.287345i	$-0.0927726\pi$
$613$	5.69615	+	9.86603i	0.230065	+	0.398485i	−0.727762	+	0.685830i	$0.759439\pi$
$614$	4.29423	+	7.43782i	0.173301	+	0.300166i
$615$		0			0
$616$			3.46410i			0.139573i
$617$	−17.6244	+	30.5263i	−0.709530	+	1.22894i	0.255502	+	0.966809i	$0.417759\pi$
$617$	−17.6244	+	30.5263i	−0.709530	+	1.22894i	−0.965032	+	0.262133i	$0.915574\pi$
$618$	9.36603	−	16.2224i	0.376757	−	0.652562i
$619$			10.5359i			0.423474i	0.977327	+	0.211737i	$0.0679119\pi$
$619$			10.5359i			0.423474i	−0.977327	+	0.211737i	$0.932088\pi$
$620$		0			0
$621$	−3.09808	−	5.36603i	−0.124322	−	0.215331i
$622$	7.83013	+	13.5622i	0.313959	+	0.543794i
$623$			1.85641i			0.0743754i
$624$	3.46410	−	1.00000i	0.138675	−	0.0400320i
$625$		0			0
$626$	11.6603	−	6.73205i	0.466037	−	0.269067i
$627$	−5.19615	+	3.00000i	−0.207514	+	0.119808i
$628$	−20.4282	−	11.7942i	−0.815174	−	0.470641i
$629$			23.7321i			0.946259i
$630$		0			0
$631$	41.3205	+	23.8564i	1.64494	+	0.949709i	0.979039	+	0.203671i	$0.0652874\pi$
$631$	41.3205	+	23.8564i	1.64494	+	0.949709i	0.665904	+	0.746037i	$0.268046\pi$
$632$	9.46410			0.376462
$633$	3.80385	+	2.19615i	0.151189	+	0.0872892i
$634$	−1.66987	−	2.89230i	−0.0663191	−	0.114868i
$635$		0			0
$636$	−0.464102			−0.0184028
$637$	−22.6244	−	5.59808i	−0.896410	−	0.221804i
$638$			11.6603i			0.461634i
$639$	−1.09808	+	0.633975i	−0.0434392	+	0.0250796i
$640$		0			0
$641$	12.9904	−	22.5000i	0.513089	−	0.888697i	−0.486796	−	0.873516i	$-0.661834\pi$
$641$	12.9904	−	22.5000i	0.513089	−	0.888697i	0.999885	−	0.0151806i	$-0.00483233\pi$
$642$	−0.196152			−0.00774152
$643$	6.92820	−	12.0000i	0.273222	−	0.473234i	−0.696463	−	0.717592i	$-0.745244\pi$
$643$	6.92820	−	12.0000i	0.273222	−	0.473234i	0.969685	+	0.244359i	$0.0785774\pi$
$644$	3.92820	+	2.26795i	0.154793	+	0.0893697i
$645$		0			0
$646$	1.43782	−	2.49038i	0.0565704	−	0.0979827i
$647$	22.7321	−	13.1244i	0.893689	−	0.515972i	0.0185417	−	0.999828i	$-0.494098\pi$
$647$	22.7321	−	13.1244i	0.893689	−	0.515972i	0.875147	+	0.483856i	$0.160764\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	37.8564			1.48599
$650$		0			0
$651$	−4.00000			−0.156772
$652$	3.26795	+	5.66025i	0.127983	+	0.221673i
$653$	−9.12436	+	5.26795i	−0.357064	+	0.206151i	−0.667792	−	0.744348i	$-0.732760\pi$
$653$	−9.12436	+	5.26795i	−0.357064	+	0.206151i	0.310728	+	0.950499i	$0.399427\pi$
$654$	2.73205	−	4.73205i	0.106832	−	0.185038i
$655$		0			0
$656$	−9.86603	−	5.69615i	−0.385204	−	0.222397i
$657$	−4.86603	+	8.42820i	−0.189842	+	0.328816i
$658$	−6.00000			−0.233904
$659$	19.1244	−	33.1244i	0.744979	−	1.29034i	−0.205225	−	0.978715i	$-0.565793\pi$
$659$	19.1244	−	33.1244i	0.744979	−	1.29034i	0.950205	−	0.311627i	$-0.100874\pi$
$660$		0			0
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	−0.333401	−	0.942785i	$-0.608196\pi$
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	0.649776	+	0.760126i	$0.274863\pi$
$662$			20.0000i			0.777322i
$663$	−5.66987	+	5.89230i	−0.220200	+	0.228838i
$664$	−10.1962			−0.395687
$665$		0			0
$666$	−5.23205	−	9.06218i	−0.202738	−	0.351152i
$667$	13.2224	+	7.63397i	0.511975	+	0.295589i
$668$	2.53590			0.0981169
$669$	−11.3205	−	6.53590i	−0.437676	−	0.252692i
$670$		0			0
$671$		−	5.66025i		−	0.218512i
$672$	0.633975	+	0.366025i	0.0244561	+	0.0141197i
$673$	−12.1865	+	7.03590i	−0.469756	+	0.271214i	−0.716138	−	0.697959i	$-0.754092\pi$
$673$	−12.1865	+	7.03590i	−0.469756	+	0.271214i	0.246381	+	0.969173i	$0.420758\pi$
$674$	5.93782	−	3.42820i	0.228716	−	0.132049i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$			38.5359i			1.48105i	0.672026	+	0.740527i	$0.265424\pi$
$677$			38.5359i			1.48105i	−0.672026	+	0.740527i	$0.734576\pi$
$678$	−9.33013	−	16.1603i	−0.358321	−	0.620631i
$679$	−2.19615	−	3.80385i	−0.0842806	−	0.145978i
$680$		0			0
$681$		−	1.80385i		−	0.0691236i
$682$	12.9282	−	22.3923i	0.495046	−	0.857446i
$683$	18.9282	−	32.7846i	0.724268	−	1.25447i	−0.235007	−	0.971994i	$-0.575511\pi$
$683$	18.9282	−	32.7846i	0.724268	−	1.25447i	0.959275	−	0.282475i	$-0.0911553\pi$
$684$			1.26795i			0.0484812i
$685$		0			0
$686$	−4.92820	−	8.53590i	−0.188160	−	0.325902i
$687$	7.92820	+	13.7321i	0.302480	+	0.523910i
$688$		−	7.66025i		−	0.292044i
$689$	−1.20577	−	1.16025i	−0.0459362	−	0.0442022i
$690$		0			0
$691$	22.8109	−	13.1699i	0.867767	−	0.501006i	0.00116153	−	0.999999i	$-0.499630\pi$
$691$	22.8109	−	13.1699i	0.867767	−	0.501006i	0.866606	+	0.498994i	$0.166297\pi$
$692$	14.1962	−	8.19615i	0.539657	−	0.311571i
$693$	3.00000	+	1.73205i	0.113961	+	0.0657952i
$694$		−	8.87564i		−	0.336915i
$695$		0			0
$696$	2.13397	+	1.23205i	0.0808881	+	0.0467008i
$697$	25.8372			0.978653
$698$	16.7321	+	9.66025i	0.633317	+	0.365646i
$699$	−9.92820	−	17.1962i	−0.375519	−	0.650418i
$700$		0			0
$701$	−31.3205			−1.18296			−0.591480	−	0.806320i	$-0.701456\pi$
$701$	−31.3205			−1.18296			−0.591480	+	0.806320i	$0.701456\pi$
$702$	0.866025	−	3.50000i	0.0326860	−	0.132099i
$703$			13.2679i			0.500410i
$704$	−4.09808	+	2.36603i	−0.154452	+	0.0891729i
$705$		0			0
$706$	9.89230	−	17.1340i	0.372302	−	0.644846i
$707$	−8.73205			−0.328403
$708$	4.00000	−	6.92820i	0.150329	−	0.260378i
$709$	−35.3827	−	20.4282i	−1.32882	−	0.767197i	−0.343707	−	0.939077i	$-0.611683\pi$
$709$	−35.3827	−	20.4282i	−1.32882	−	0.767197i	−0.985118	+	0.171880i	$0.945016\pi$
$710$		0			0
$711$	4.73205	−	8.19615i	0.177466	−	0.307380i
$712$	−2.19615	+	1.26795i	−0.0823043	+	0.0475184i
$713$	−16.9282	−	29.3205i	−0.633966	−	1.09806i
$714$	−1.66025			−0.0621334
$715$		0			0
$716$	22.0526			0.824143
$717$	4.83013	+	8.36603i	0.180384	+	0.312435i
$718$	20.0263	−	11.5622i	0.747374	−	0.431497i
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	−0.575737	−	0.817635i	$-0.695285\pi$
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	0.995961	+	0.0897860i	$0.0286183\pi$
$720$		0			0
$721$	11.8756	+	6.85641i	0.442272	+	0.255346i
$722$	−8.69615	+	15.0622i	−0.323637	+	0.560556i
$723$	−17.5885			−0.654122
$724$	4.40192	−	7.62436i	0.163596	−	0.283357i
$725$		0			0
$726$	−9.86603	+	5.69615i	−0.366163	+	0.211404i
$727$			20.9808i			0.778133i	0.921210	+	0.389067i	$0.127202\pi$
$727$			20.9808i			0.778133i	−0.921210	+	0.389067i	$0.872798\pi$
$728$	0.732051	+	2.53590i	0.0271316	+	0.0939866i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.68653	+	15.0455i	0.321283	+	0.556479i
$732$	−1.03590	−	0.598076i	−0.0382879	−	0.0221055i
$733$	−19.0000			−0.701781			−0.350891	−	0.936416i	$-0.614121\pi$
$733$	−19.0000			−0.701781			−0.350891	+	0.936416i	$0.614121\pi$
$734$	−12.7583	−	7.36603i	−0.470919	−	0.271885i
$735$		0			0
$736$			6.19615i			0.228393i
$737$	−45.5885	−	26.3205i	−1.67927	−	0.969528i
$738$	−9.86603	+	5.69615i	−0.363173	+	0.209678i
$739$	−9.46410	+	5.46410i	−0.348143	+	0.201000i	−0.663867	−	0.747851i	$-0.731086\pi$
$739$	−9.46410	+	5.46410i	−0.348143	+	0.201000i	0.315724	+	0.948851i	$0.397753\pi$
$740$		0			0
$741$	−3.16987	+	3.29423i	−0.116448	+	0.121017i
$742$		−	0.339746i		−	0.0124725i
$743$	−13.8038	−	23.9090i	−0.506414	−	0.877135i	−0.999972	−	0.00742221i	$-0.997637\pi$
$743$	−13.8038	−	23.9090i	−0.506414	−	0.877135i	0.493558	−	0.869713i	$-0.335696\pi$
$744$	−2.73205	−	4.73205i	−0.100162	−	0.173485i
$745$		0			0
$746$		−	10.2679i		−	0.375936i
$747$	−5.09808	+	8.83013i	−0.186529	+	0.323077i
$748$	5.36603	−	9.29423i	0.196201	−	0.339831i
$749$		−	0.143594i		−	0.00524679i
$750$		0			0
$751$	7.95448	+	13.7776i	0.290263	+	0.502751i	0.973872	−	0.227098i	$-0.0729238\pi$
$751$	7.95448	+	13.7776i	0.290263	+	0.502751i	−0.683609	+	0.729849i	$0.739590\pi$
$752$	−4.09808	−	7.09808i	−0.149441	−	0.258840i
$753$		−	6.53590i		−	0.238181i
$754$	2.46410	+	8.53590i	0.0897373	+	0.310859i
$755$		0			0
$756$	0.633975	−	0.366025i	0.0230574	−	0.0133122i
$757$	−6.12436	+	3.53590i	−0.222593	+	0.128514i	−0.607151	−	0.794587i	$-0.707688\pi$
$757$	−6.12436	+	3.53590i	−0.222593	+	0.128514i	0.384557	+	0.923101i	$0.374354\pi$
$758$	1.26795	+	0.732051i	0.0460540	+	0.0265893i
$759$			29.3205i			1.06427i
$760$		0			0
$761$	−20.1962	−	11.6603i	−0.732110	−	0.422684i	0.0870836	−	0.996201i	$-0.472245\pi$
$761$	−20.1962	−	11.6603i	−0.732110	−	0.422684i	−0.819194	+	0.573517i	$0.805579\pi$
$762$	−17.8564			−0.646869
$763$	3.46410	+	2.00000i	0.125409	+	0.0724049i
$764$	−3.46410	−	6.00000i	−0.125327	−	0.217072i
$765$		0			0
$766$	−5.46410			−0.197426
$767$	27.7128	−	8.00000i	1.00065	−	0.288863i
$768$			1.00000i			0.0360844i
$769$	13.9808	−	8.07180i	0.504159	−	0.291076i	−0.226270	−	0.974065i	$-0.572653\pi$
$769$	13.9808	−	8.07180i	0.504159	−	0.291076i	0.730429	+	0.682988i	$0.239320\pi$
$770$		0			0
$771$	13.3301	−	23.0885i	0.480073	−	0.831510i
$772$	−8.26795			−0.297570
$773$	−17.5359	+	30.3731i	−0.630722	+	1.09244i	0.356682	+	0.934226i	$0.383908\pi$
$773$	−17.5359	+	30.3731i	−0.630722	+	1.09244i	−0.987404	+	0.158217i	$0.949425\pi$
$774$	−6.63397	−	3.83013i	−0.238453	−	0.137671i
$775$		0			0
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	6.63397	−	3.83013i	0.237993	−	0.137405i
$778$	14.8923	+	25.7942i	0.533915	+	0.924768i
$779$	14.4449			0.517541
$780$		0			0
$781$	6.00000			0.214697
$782$	−7.02628	−	12.1699i	−0.251259	−	0.435194i
$783$	2.13397	−	1.23205i	0.0762620	−	0.0440299i
$784$	3.23205	−	5.59808i	0.115430	−	0.199931i
$785$		0			0
$786$	−11.6603	−	6.73205i	−0.415907	−	0.240124i
$787$	19.6603	−	34.0526i	0.700812	−	1.21384i	−0.267369	−	0.963594i	$-0.586154\pi$
$787$	19.6603	−	34.0526i	0.700812	−	1.21384i	0.968182	−	0.250248i	$-0.0805123\pi$
$788$	9.85641			0.351120
$789$	14.0263	−	24.2942i	0.499349	−	0.864897i
$790$		0			0
$791$	11.8301	−	6.83013i	0.420631	−	0.242851i
$792$			4.73205i			0.168146i
$793$	−1.19615	−	4.14359i	−0.0424766	−	0.147143i
$794$	0.392305			0.0139224
$795$		0			0
$796$	1.90192	+	3.29423i	0.0674119	+	0.116761i
$797$	29.4449	+	17.0000i	1.04299	+	0.602171i	0.920679	−	0.390321i	$-0.127636\pi$
$797$	29.4449	+	17.0000i	1.04299	+	0.602171i	0.122312	+	0.992492i	$0.460969\pi$
$798$	−0.928203			−0.0328580
$799$	16.0981	+	9.29423i	0.569509	+	0.328806i
$800$		0			0
$801$			2.53590i			0.0896016i
$802$	18.9904	+	10.9641i	0.670574	+	0.387156i
$803$	39.8827	−	23.0263i	1.40743	−	0.812580i
$804$	−9.63397	+	5.56218i	−0.339764	+	0.196163i
$805$		0			0
$806$	4.73205	−	19.1244i	0.166679	−	0.673627i
$807$			1.46410i			0.0515388i
$808$	−5.96410	−	10.3301i	−0.209816	−	0.363413i
$809$	−11.2058	−	19.4090i	−0.393974	−	0.682383i	0.598996	−	0.800752i	$-0.295567\pi$
$809$	−11.2058	−	19.4090i	−0.393974	−	0.682383i	−0.992970	+	0.118369i	$0.962233\pi$
$810$		0			0
$811$		−	45.1769i		−	1.58638i	−0.608977	−	0.793188i	$-0.708420\pi$
$811$		−	45.1769i		−	1.58638i	0.608977	−	0.793188i	$-0.291580\pi$
$812$	−0.901924	+	1.56218i	−0.0316513	+	0.0548217i
$813$	−2.92820	+	5.07180i	−0.102697	+	0.177876i
$814$			49.5167i			1.73556i
$815$		0			0
$816$	−1.13397	−	1.96410i	−0.0396971	−	0.0687573i
$817$	4.85641	+	8.41154i	0.169904	+	0.294283i
$818$		−	14.2679i		−	0.498867i
$819$	2.56218	+	0.633975i	0.0895297	+	0.0221529i
$820$		0			0
$821$	11.1962	−	6.46410i	0.390748	−	0.225599i	−0.291736	−	0.956499i	$-0.594233\pi$
$821$	11.1962	−	6.46410i	0.390748	−	0.225599i	0.682484	+	0.730900i	$0.260900\pi$
$822$	1.66987	−	0.964102i	0.0582435	−	0.0336269i
$823$	−36.0000	−	20.7846i	−1.25488	−	0.724506i	−0.282806	−	0.959177i	$-0.591265\pi$
$823$	−36.0000	−	20.7846i	−1.25488	−	0.724506i	−0.972075	+	0.234671i	$0.924599\pi$
$824$			18.7321i			0.652562i
$825$		0			0
$826$	5.07180	+	2.92820i	0.176470	+	0.101885i
$827$	−33.4641			−1.16366			−0.581830	−	0.813310i	$-0.697663\pi$
$827$	−33.4641			−1.16366			−0.581830	+	0.813310i	$0.697663\pi$
$828$	5.36603	+	3.09808i	0.186482	+	0.107666i
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	0.741338	−	0.671132i	$-0.234192\pi$
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	−0.951886	+	0.306452i	$0.900858\pi$
$830$		0			0
$831$	2.26795			0.0786743
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$			14.6603i			0.507948i
$834$	8.53590	−	4.92820i	0.295574	−	0.170650i
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	−5.46410			−0.188867
$838$	−5.26795	+	9.12436i	−0.181978	+	0.315196i
$839$	−12.2487	−	7.07180i	−0.422872	−	0.244146i	0.273433	−	0.961891i	$-0.411841\pi$
$839$	−12.2487	−	7.07180i	−0.422872	−	0.244146i	−0.696306	+	0.717745i	$0.745174\pi$
$840$		0			0
$841$	11.4641	−	19.8564i	0.395314	−	0.684704i
$842$	28.3301	−	16.3564i	0.976321	−	0.563679i
$843$	11.1603	+	19.3301i	0.384380	+	0.665765i
$844$	−4.39230			−0.151189
$845$		0			0
$846$	−8.19615			−0.281790
$847$	−4.16987	−	7.22243i	−0.143279	−	0.248166i
$848$	0.401924	−	0.232051i	0.0138021	−	0.00796866i
$849$	−4.16987	+	7.22243i	−0.143110	+	0.247873i
$850$		0			0
$851$	56.1506	+	32.4186i	1.92482	+	1.11129i
$852$	0.633975	−	1.09808i	0.0217196	−	0.0376195i
$853$	8.17691			0.279972			0.139986	−	0.990153i	$-0.455294\pi$
$853$	8.17691			0.279972			0.139986	+	0.990153i	$0.455294\pi$
$854$	0.437822	−	0.758330i	0.0149820	−	0.0259495i
$855$		0			0
$856$	0.169873	−	0.0980762i	0.00580614	−	0.00335218i
$857$		−	19.4449i		−	0.664224i	−0.943240	−	0.332112i	$-0.892239\pi$
$857$		−	19.4449i		−	0.664224i	0.943240	−	0.332112i	$-0.107761\pi$
$858$	−11.8301	+	12.2942i	−0.403874	+	0.419718i
$859$	22.8756			0.780507			0.390253	−	0.920707i	$-0.372387\pi$
$859$	22.8756			0.780507			0.390253	+	0.920707i	$0.372387\pi$
$860$		0			0
$861$	−4.16987	−	7.22243i	−0.142109	−	0.246140i
$862$	9.63397	+	5.56218i	0.328134	+	0.189449i
$863$	−7.12436			−0.242516			−0.121258	−	0.992621i	$-0.538693\pi$
$863$	−7.12436			−0.242516			−0.121258	+	0.992621i	$0.538693\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			14.8564i			0.504841i
$867$	−10.2679	−	5.92820i	−0.348718	−	0.201332i
$868$	3.46410	−	2.00000i	0.117579	−	0.0678844i
$869$	−38.7846	+	22.3923i	−1.31568	+	0.759607i
$870$		0			0
$871$	−38.9352	−	9.63397i	−1.31927	−	0.326435i
$872$			5.46410i			0.185038i
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$	−3.92820	−	6.80385i	−0.132873	−	0.230144i
$875$		0			0
$876$		−	9.73205i		−	0.328816i
$877$	−5.03590	+	8.72243i	−0.170050	+	0.294536i	−0.938437	−	0.345450i	$-0.887726\pi$
$877$	−5.03590	+	8.72243i	−0.170050	+	0.294536i	0.768387	+	0.639985i	$0.221060\pi$
$878$	8.83013	−	15.2942i	0.298002	−	0.516155i
$879$		−	14.5167i		−	0.489635i
$880$		0			0
$881$	25.9186	+	44.8923i	0.873219	+	1.51246i	0.858648	+	0.512566i	$0.171305\pi$
$881$	25.9186	+	44.8923i	0.873219	+	1.51246i	0.0145717	+	0.999894i	$0.495362\pi$
$882$	−3.23205	−	5.59808i	−0.108829	−	0.188497i
$883$		−	29.0718i		−	0.978344i	−0.872187	−	0.489172i	$-0.837299\pi$
$883$		−	29.0718i		−	0.978344i	0.872187	−	0.489172i	$-0.162701\pi$
$884$	1.96410	−	7.93782i	0.0660599	−	0.266978i
$885$		0			0
$886$	31.5167	−	18.1962i	1.05882	−	0.611312i
$887$	−8.78461	+	5.07180i	−0.294958	+	0.170294i	−0.640176	−	0.768228i	$-0.721138\pi$
$887$	−8.78461	+	5.07180i	−0.294958	+	0.170294i	0.345217	+	0.938523i	$0.387805\pi$
$888$	9.06218	+	5.23205i	0.304107	+	0.175576i
$889$		−	13.0718i		−	0.438414i
$890$		0			0
$891$	4.09808	+	2.36603i	0.137291	+	0.0792648i
$892$	13.0718			0.437676
$893$	9.00000	+	5.19615i	0.301174	+	0.173883i
$894$	−1.40192	−	2.42820i	−0.0468873	−	0.0812113i
$895$		0			0
$896$	−0.732051			−0.0244561
$897$	6.19615	+	21.4641i	0.206884	+	0.716665i
$898$		−	23.3205i		−	0.778215i
$899$	11.6603	−	6.73205i	0.388891	−	0.224526i
$900$		0			0
$901$	−0.526279	+	0.911543i	−0.0175329	+	0.0303679i
$902$	53.9090			1.79497
$903$	2.80385	−	4.85641i	0.0933062	−	0.161611i
$904$	16.1603	+	9.33013i	0.537482	+	0.310315i
$905$		0			0
$906$	−1.63397	+	2.83013i	−0.0542852	+	0.0940247i
$907$	13.5167	−	7.80385i	0.448813	−	0.259123i	−0.258516	−	0.966007i	$-0.583233\pi$
$907$	13.5167	−	7.80385i	0.448813	−	0.259123i	0.707329	+	0.706885i	$0.249900\pi$
$908$	0.901924	+	1.56218i	0.0299314	+	0.0518427i
$909$	−11.9282			−0.395634
$910$		0			0
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$	−0.633975	−	1.09808i	−0.0209930	−	0.0363609i
$913$	41.7846	−	24.1244i	1.38287	−	0.798400i
$914$	−9.33013	+	16.1603i	−0.308613	+	0.534534i
$915$		0			0
$916$	−13.7321	−	7.92820i	−0.453720	−	0.261955i
$917$	4.92820	−	8.53590i	0.162744	−	0.281880i
$918$	−2.26795			−0.0748535
$919$	−28.9808	+	50.1962i	−0.955987	+	1.65582i	−0.223894	+	0.974613i	$0.571877\pi$
$919$	−28.9808	+	50.1962i	−0.955987	+	1.65582i	−0.732093	+	0.681205i	$0.761456\pi$
$920$		0			0
$921$	−7.43782	+	4.29423i	−0.245085	+	0.141500i
$922$			25.7321i			0.847440i
$923$	4.39230	−	1.26795i	0.144574	−	0.0417351i
$924$	−3.46410			−0.113961
$925$		0			0
$926$	14.0263	+	24.2942i	0.460932	+	0.798358i
$927$	16.2224	+	9.36603i	0.532815	+	0.307621i
$928$	−2.46410			−0.0808881
$929$	8.00962	+	4.62436i	0.262787	+	0.151720i	0.625605	−	0.780140i	$-0.284852\pi$
$929$	8.00962	+	4.62436i	0.262787	+	0.151720i	−0.362818	+	0.931860i	$0.618185\pi$
$930$		0			0
$931$			8.19615i			0.268618i
$932$	17.1962	+	9.92820i	0.563279	+	0.325209i
$933$	−13.5622	+	7.83013i	−0.444006	+	0.256347i
$934$	−10.9019	+	6.29423i	−0.356722	+	0.205953i
$935$		0			0
$936$	1.00000	+	3.46410i	0.0326860	+	0.113228i
$937$		−	43.2487i		−	1.41287i	−0.707776	−	0.706437i	$-0.750301\pi$
$937$		−	43.2487i		−	1.41287i	0.707776	−	0.706437i	$-0.249699\pi$
$938$	−4.07180	−	7.05256i	−0.132949	−	0.230274i
$939$	6.73205	+	11.6603i	0.219692	+	0.380518i
$940$		0			0
$941$		−	56.6410i		−	1.84644i	−0.384267	−	0.923222i	$-0.625546\pi$
$941$		−	56.6410i		−	1.84644i	0.384267	−	0.923222i	$-0.374454\pi$
$942$	11.7942	−	20.4282i	0.384277	−	0.665587i
$943$	35.2942	−	61.1314i	1.14934	−	1.99071i
$944$			8.00000i			0.260378i
$945$		0			0
$946$	18.1244	+	31.3923i	0.589274	+	1.02065i
$947$	17.4641	+	30.2487i	0.567507	+	0.982951i	0.996812	+	0.0797913i	$0.0254254\pi$
$947$	17.4641	+	30.2487i	0.567507	+	0.982951i	−0.429305	+	0.903160i	$0.641241\pi$
$948$			9.46410i			0.307380i
$949$	24.3301	−	25.2846i	0.789789	−	0.820773i
$950$		0			0
$951$	2.89230	−	1.66987i	0.0937894	−	0.0541493i
$952$	1.43782	−	0.830127i	0.0466001	−	0.0269046i
$953$	−36.0000	−	20.7846i	−1.16615	−	0.673280i	−0.213383	−	0.976969i	$-0.568448\pi$
$953$	−36.0000	−	20.7846i	−1.16615	−	0.673280i	−0.952771	+	0.303689i	$0.901782\pi$
$954$		−	0.464102i		−	0.0150258i
$955$		0			0
$956$	−8.36603	−	4.83013i	−0.270577	−	0.156217i
$957$	−11.6603			−0.376922
$958$	−22.9808	−	13.2679i	−0.742475	−	0.428668i
$959$	0.705771	+	1.22243i	0.0227905	+	0.0394744i
$960$		0			0
$961$	1.14359			0.0368901
$962$	10.4641	+	36.2487i	0.337376	+	1.16871i
$963$		−	0.196152i		−	0.00632092i
$964$	15.2321	−	8.79423i	0.490591	−	0.283243i
$965$		0			0
$966$	−2.26795	+	3.92820i	−0.0729701	+	0.126388i
$967$	−18.8756			−0.607000			−0.303500	−	0.952831i	$-0.598155\pi$
$967$	−18.8756			−0.607000			−0.303500	+	0.952831i	$0.598155\pi$
$968$	5.69615	−	9.86603i	0.183081	−	0.317106i
$969$	2.49038	+	1.43782i	0.0800026	+	0.0461895i
$970$		0			0
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	−0.681660	−	0.731669i	$-0.738741\pi$
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	0.974474	+	0.224500i	$0.0720748\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	3.60770	+	6.24871i	0.115657	+	0.200324i
$974$	21.1244			0.676868
$975$		0			0
$976$	1.19615			0.0382879
$977$	−16.0359	−	27.7750i	−0.513034	−	0.888601i	−0.999886	−	0.0151161i	$-0.995188\pi$
$977$	−16.0359	−	27.7750i	−0.513034	−	0.888601i	0.486852	−	0.873485i	$-0.338145\pi$
$978$	−5.66025	+	3.26795i	−0.180995	+	0.104497i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	4.73205	+	2.73205i	0.151083	+	0.0872277i
$982$	2.63397	−	4.56218i	0.0840535	−	0.145585i
$983$	−20.7846			−0.662926			−0.331463	−	0.943468i	$-0.607542\pi$
$983$	−20.7846			−0.662926			−0.331463	+	0.943468i	$0.607542\pi$
$984$	5.69615	−	9.86603i	0.181587	−	0.314517i
$985$		0			0
$986$	4.83975	−	2.79423i	0.154129	−	0.0889864i
$987$		−	6.00000i		−	0.190982i
$988$	1.09808	−	4.43782i	0.0349345	−	0.141186i
$989$	47.4641			1.50927
$990$		0			0
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	0.926135	−	0.377191i	$-0.123110\pi$
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	−0.789725	+	0.613461i	$0.789777\pi$
$992$	4.73205	+	2.73205i	0.150243	+	0.0867427i
$993$	−20.0000			−0.634681
$994$	0.803848	+	0.464102i	0.0254965	+	0.0147204i
$995$		0			0
$996$		−	10.1962i		−	0.323077i
$997$	33.4808	+	19.3301i	1.06035	+	0.612191i	0.925528	−	0.378679i	$-0.123622\pi$
$997$	33.4808	+	19.3301i	1.06035	+	0.612191i	0.134818	+	0.990870i	$0.456955\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$	9.06218	−	5.23205i	0.286715	−	0.165535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.b.49.2		4
5.2	odd	4		78.2.i.a.49.2	yes	4
5.3	odd	4		1950.2.bc.d.751.1		4
5.4	even	2		1950.2.y.g.49.1		4
13.4	even	6		1950.2.y.g.199.1		4
15.2	even	4		234.2.l.c.127.1		4
20.7	even	4		624.2.bv.e.49.2		4
60.47	odd	4		1872.2.by.h.1297.1		4
65.2	even	12		1014.2.a.k.1.1		2
65.4	even	6	inner	1950.2.y.b.199.2		4
65.7	even	12		1014.2.e.i.529.2		4
65.12	odd	4		1014.2.i.a.361.1		4
65.17	odd	12		78.2.i.a.43.2	✓	4
65.22	odd	12		1014.2.i.a.823.1		4
65.32	even	12		1014.2.e.g.529.1		4
65.37	even	12		1014.2.a.i.1.2		2
65.42	odd	12		1014.2.b.e.337.3		4
65.43	odd	12		1950.2.bc.d.901.1		4
65.47	even	4		1014.2.e.i.991.2		4
65.57	even	4		1014.2.e.g.991.1		4
65.62	odd	12		1014.2.b.e.337.2		4
195.2	odd	12		3042.2.a.p.1.2		2
195.17	even	12		234.2.l.c.199.1		4
195.62	even	12		3042.2.b.i.1351.3		4
195.107	even	12		3042.2.b.i.1351.2		4
195.167	odd	12		3042.2.a.y.1.1		2
260.67	odd	12		8112.2.a.bp.1.1		2
260.147	even	12		624.2.bv.e.433.1		4
260.167	odd	12		8112.2.a.bj.1.2		2
780.407	odd	12		1872.2.by.h.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	65.17	odd	12
78.2.i.a.49.2	yes	4	5.2	odd	4
234.2.l.c.127.1		4	15.2	even	4
234.2.l.c.199.1		4	195.17	even	12
624.2.bv.e.49.2		4	20.7	even	4
624.2.bv.e.433.1		4	260.147	even	12
1014.2.a.i.1.2		2	65.37	even	12
1014.2.a.k.1.1		2	65.2	even	12
1014.2.b.e.337.2		4	65.62	odd	12
1014.2.b.e.337.3		4	65.42	odd	12
1014.2.e.g.529.1		4	65.32	even	12
1014.2.e.g.991.1		4	65.57	even	4
1014.2.e.i.529.2		4	65.7	even	12
1014.2.e.i.991.2		4	65.47	even	4
1014.2.i.a.361.1		4	65.12	odd	4
1014.2.i.a.823.1		4	65.22	odd	12
1872.2.by.h.433.2		4	780.407	odd	12
1872.2.by.h.1297.1		4	60.47	odd	4
1950.2.y.b.49.2		4	1.1	even	1	trivial
1950.2.y.b.199.2		4	65.4	even	6	inner
1950.2.y.g.49.1		4	5.4	even	2
1950.2.y.g.199.1		4	13.4	even	6
1950.2.bc.d.751.1		4	5.3	odd	4
1950.2.bc.d.901.1		4	65.43	odd	12
3042.2.a.p.1.2		2	195.2	odd	12
3042.2.a.y.1.1		2	195.167	odd	12
3042.2.b.i.1351.2		4	195.107	even	12
3042.2.b.i.1351.3		4	195.62	even	12
8112.2.a.bj.1.2		2	260.167	odd	12
8112.2.a.bp.1.1		2	260.67	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.96410 + 1.13397i) q^{17} -1.00000 q^{18} +(1.09808 + 0.633975i) q^{19} -0.732051i q^{21} +(4.09808 + 2.36603i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(0.366025 + 0.633975i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.23205 + 9.06218i) q^{37} -1.26795i q^{38} +(-0.866025 + 3.50000i) q^{39} +(9.86603 - 5.69615i) q^{41} +(-0.633975 + 0.366025i) q^{42} +(6.63397 + 3.83013i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} +8.19615 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-1.00000 - 3.46410i) q^{52} +0.464102i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.366025 - 0.633975i) q^{56} +1.26795 q^{57} +(1.23205 - 2.13397i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(-4.73205 + 2.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(-1.96410 + 1.13397i) q^{68} +(3.09808 - 5.36603i) q^{69} +(-1.09808 - 0.633975i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.73205 q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410i q^{77} +(3.46410 - 1.00000i) q^{78} +9.46410 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.86603 - 5.69615i) q^{82} -10.1962 q^{83} +(0.633975 + 0.366025i) q^{84} -7.66025i q^{86} +(2.13397 + 1.23205i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615i q^{92} +(-2.73205 - 4.73205i) q^{93} +(-4.09808 - 7.09808i) q^{94} +1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33}+ \cdots + 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^11 - 10 * q^13 + 4 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 6 * q^22 + 18 * q^23 + 14 * q^26 - 2 * q^28 - 2 * q^29 - 2 * q^32 - 6 * q^33 + 2 * q^36 + 14 * q^37 + 36 * q^41 - 6 * q^42 + 30 * q^43 - 18 * q^46 + 12 * q^47 + 6 * q^49 + 16 * q^51 - 4 * q^52 - 2 * q^56 + 12 * q^57 - 2 * q^58 + 8 * q^61 - 12 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 6 * q^68 + 2 * q^69 + 6 * q^71 + 2 * q^72 - 32 * q^73 + 14 * q^74 + 6 * q^76 + 24 * q^79 - 2 * q^81 - 36 * q^82 - 20 * q^83 + 6 * q^84 + 12 * q^87 - 6 * q^88 + 12 * q^89 - 4 * q^91 - 4 * q^93 - 6 * q^94 + 12 * q^97 + 6 * q^98

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